Christopher Ray, chairman of the Headmasters’ and Headmistresses’ Conference, which represents more than 250 top independent schools, said that the use of “positive discrimination” in the admissions system risked acting against pupils from the fee-paying sector.

Currently, universities are expected to draw up targets to boost the number of pupils admitted from state schools and poor families.

But Dr Ray, High Master of Manchester Grammar School, said the process was not sophisticated enough to take account of pupils from selective state grammar schools or comprehensively-educated teenagers sent to private tutors by their parents.

The system also risks overlooking the thousands of pupils from the poorest families given bursary places at independent schools, he said.

The comments come amid continuing concerns over the use of “social engineering” in university admissions.

All institutions in England are expected to draw up “access agreements” setting out measures designed to create a more balanced student body in return for the power to charge up to £9,000 tuition fees.

As part of the document, they must set targets to boost participation rates among pupils from state schools, deprived families and neighbourhoods with a poor track record of higher education.

Prof Les Ebdon, the head of the Government’s Office for Fair Access, has told leading universities to set the most “challenging” benchmarks.

This week, it emerged that the number of private school pupils admitted to Cambridge had dropped by 18 per cent to 892 in just 12 months as the proportion of state-educated entrants rocketed to a 30-year high.

Speaking ahead of HMC’s annual conference in Belfast next week, Dr Ray said: “Without positive discrimination, we wouldn’t have had the huge advances we’ve had on the disabled front. But actually, in their case, they’ve been trying to change attitudes.

"Here, it’s not attitudes that are being suggested, it’s just straightforward favouring of those who’ve not been able to perform as well, due to the failings of the state sector, on the whole.”

He insisted there was “no evidence” that independently-educated pupils had so far been systematically denied places by the new admissions rules.

But he said the system of “positive discrimination” was inadequate when it came to properly differentiating between pupils.

Dr Ray said it struggled to give credit to teenagers on full bursaries at his private school “where reading books in the home is not part of the culture [and] where no-one else in the family has been to university”.

He also said that targets to increase state school admissions risked giving unfair advantages to those educated at highly-selective grammar schools or teenagers from state comprehensives who receive private tuition in the evenings and weekends.

“The tutoring industry is huge, not just for 11-plus but for GCSE and A-level, and I don’t understand or see how any system, however fleet of foot or focused, can actually get to that level of scrutiny," he said. "Would you actually ask your child to declare on his UCAS form that he had been tutored?

In separate comments, Dr Ray also criticised politicians who repeatedly attack private schools for failing to do enough to justify their charitable status.

This summer, Alan Milburn, the Coalition’s social mobility tsar and former Labour cabinet minister, said schools had to do more than simply opening their playing fields.

Dr Ray said: “It is a typical misrepresentation of the independent sector, hoping to gain a political advantage. I understand why politicians feel the need to do that but, of course, if they entered such answers on examination scripts they would be quite fairly be graded fail.”